The top student must be diligent.

Chapter 168 A new physical field: X-field? !

【The National Science and Technology Awards Conference was held! These three projects won the first prize of the National Natural Science Award! Click to view details →】

[The National Highest Science and Technology Award was issued. Let's see which two scientists received this honor? 】

【Goldbach's conjecture won the first prize of the National Natural Science Award, so what about the twin prime conjecture? 】

[Shocked! He actually did this at the National Science and Technology Awards Conference...]

……

After the National Science and Technology Awards Conference came to an end, major news media also released related news, and the discussion on the Internet was also very heated.

On Weibo, #National Science and Technology Awards Conference# was on the hot search list. In addition, #Goldbach's Conjecture# also made it to the hot search list separately.

As for the other two first prizes, there were none, probably because Xiao Yi himself had a lot of traffic.

Of course, the more important question is why netizens are wondering why the twin prime conjecture did not win the prize.

[The status of the twin prime conjecture in the mathematical world should be similar to that of the Goldbach conjecture? Shouldn't this win another first prize? ]

[Come on, what kind of award is the Natural Science Award? It's already a historic achievement to have three winners this year.]

[There is a reason for choosing Ge Chai. After all, Ge Chai's lecture was held in our Great Hall of the People, and it has such a great influence in China. I can only say that Xiao Shen is awesome. He won the first prize in natural science at the age of 18.]

[And it was the first prize in mathematics. The last time I won the first prize in mathematics was in 97. Strictly speaking, that project was not pure mathematics, but computational mathematics.]

【纯数学的一等奖太难得了，最早好像还是陈景润先生的1+2定理获得过吧？现在是从1+2变成了1+1，历史的回旋镖了属于是。】

[I feel like the first prize will often be won by Xiao Shen in the future. Maybe next year it will be the twin prime conjecture.]

[There will be no awards next year. There is news that it will be changed to every three years. The next one will probably be in November 2024. ]

[Oh my god, wait so long? ]

[The selection will be more difficult in the future. This is also a reform of the country's domestic award selection. Only projects with real quality can pass. I guess I was able to win the award in the same year I completed it, probably because the next time will be three years later.]

[That’s good. With so many awards nowadays, it’s hard to guarantee that there won’t be some fake ones…]
……

There were heated discussions online, but no one was paying attention to Xiao Yi, who had just received his award and returned to the Basic Science Park.

For him, the current priority is to study the quality gap problem.

After returning to the dormitory, Xiao Yi once again thought about which angle to use to solve the problem.

This time, his attention turned to the direction of TQFT.

TQFT, topological quantum field theory, emphasizes the topological properties of quantum field theory rather than its metric properties, and is also a very powerful physics tool.

During his research, Xiao Yi began to think about the topological invariants of Yang-Mills theory and its behavior in different topological spaces.

"According to Chern-Simons theory, the moduli space Σ of the Yang-Mills equations on a compact Riemann surface can be viewed as the configuration space Σ×[0, 1] of the Chern-Simons theory on a cylinder. In this case, the moduli space can be geometrically quantized...geometrically quantized?"

Finally, on a cold winter night, in a warm dormitory with the heating on full blast, Xiao Yi's boiling brain suddenly calmed down at this moment.

However, beneath the tranquil surface, there is a more powerful surge hidden.

"Doesn't this mean that, after introducing the Chern number, the mass gap problem of Yang-Mills theory can be transformed into an existence problem about topological invariants?"

There seemed to be a gleam of wisdom in his eyes.

The pen tip began to move on the draft paper.

And time passed again.

Just like that, four months passed quietly.

……

The time has come to the end of February 2022.

The Spring Festival has passed, and the Lantern Festival ended two weeks ago. Students have returned to their schools to start classes, and the cogs of society have returned to their posts and begun to contribute their own efforts to the operation of the entire world.

On February 2, a new issue of Science magazine was published. On the cover, a huge W crushed the disk representing the major elementary particles in the standard model.

At the bottom, there are two lines of letters explaining the meaning of this cover.

[Super heavy! W boson mass measured higher than expected! ]

[From the cover of the April 2022, 4 issue of Science magazine. The supermass of the W boson is also a real thing in the physics world. (The time was slightly photoshopped, so it’s a little distorted)]

With the release of this issue, it immediately set off the entire physics community.

There is no doubt that what this cover represents is that the cooperation between the Institute of High Energy Physics of China and CERN has been completed, and their final result is the same as what Xiao Yi predicted at the beginning!
The W boson is indeed overweight!

For a moment, all physicists around the world were excited by this news.

On major forums, discussions have once again become fierce.

[Oh my god! This is real! CERN and the Institute of High Energy Physics of China have calculated a total of 100 million sets of signal data about the W boson! This time it is definitely credible! ]

[I have read the paper. According to the results, the mass of the W boson is 40844±6MeV. Damn, Xiao Yi's previous paper had 2000 data sets, but it just exceeded 5 standard deviations. Now it has 100 million data sets, which is more than 10 standard deviations. There must be something wrong here, right?]

[It’s incredible. Our research team is already preparing to go to CERN. I guess CERN will be very busy in the next period of time.]

[Can someone tell me what the reason for being overweight is?! Damn, will I really be able to encounter a major event in the field of physics in my lifetime? ]

[Wasn’t the Higgs boson a big enough event back then? 】

[When the Higgs boson was discovered, I was still a high school student and had no idea what high-energy physics was.]

[Hey, maybe it's caused by supersymmetric particles? ]

【We can only look forward to the final conclusion. 】

……

Amidst all the discussions, an extremely important meeting was being held at the European Organization for Nuclear Research. The meeting was discussing this very conclusion.

"…We mainly used Shaw's error analysis theory to process 100 million sets of W boson signal data and came to this final conclusion. Now we have sufficient reason to believe that the actual mass of the W boson exceeds the prediction of the standard model."

In the conference room, Professor Frank Wilczek, Nobel Prize winner and the main person in charge of the W boson mass verification project, was giving a report.

"I think this is one of the most important discoveries in the field of particles since the discovery of the Higgs boson, so it is necessary for CERN to continue to study the supermassive W boson as a priority. Maybe this will lead to the discovery of another theory of relativity?"

"No one can tell."

After Professor Wilczek finished his speech, he won applause from many physicists present.

At this time, CERN's Director General, Fabiola Gianotti, asked: "Professor Wilczek, can you tell me more about the statistical method you used? Is it really effective? Is it really credible? I have always been curious about why this statistical method can give us such a huge difference in results from previous statistical methods."

Hearing this question, Wilczek smiled and said, "Professor Gianotti, we have discussed this question many times over the past few months. We have also answered why this new statistical method shows such a difference. The first problem lies in its more sophisticated handling of errors."

"Precision is crucial, and the mathematical methods used here are also advanced enough."

"In addition, one thing I must point out is that the difference between the results of previous statistical methods and current statistical methods is actually not huge."

"The difference between the two results is only 0.1%, but when observed at a microscopic scale, the difference becomes huge, just like 0.1% of a W boson is almost equal to the mass of 157 electrons."

"But that's how high-energy physics works. In other physics, any difference may be considered an error, but in high-energy physics, there are many things to consider."

“It’s like the 5σ rule, which was proposed by high-energy physics.”

"I believe Professor Edward Witten would agree with this."

Everyone looked at an old man sitting in a seat in the conference room. Professor Edward Witten was sitting in that seat.

Hearing Wilczek suddenly cue him, Witten smiled and then said, "Yes, I agree with Frank."

There was immediate applause in the conference room.

Obviously, there are still quite a few researchers who agree that the problem of W boson supermass should be CERN's main goal for the next period of time.

Regardless of whether it is Wilczek or Witten, both of them are considered to be the highest representatives of physics and mathematical ability among all the people present, and their opinions are extremely important.

Seeing this, Director General Fabiola Gianotti said nothing more, nodded and said: "In this case, the issue of [whether to make the W boson mass verification project the next primary scientific goal of CERN] is passed."

Then, she turned to look at the other side of the conference room and said, "Professor Tang, are you willing to continue to participate in this research?"

On the other side, sitting there were Tang Yifang and other researchers from the Chinese Institute of High Energy Physics. As partners on this project, they were also invited here by CERN.

Tang Yifang stood up, nodded with a smile, and said, "On behalf of the Institute of High Energy Physics of China, I am willing to join the cooperation."

Such research projects would generally be monopolized by CERN, so it is naturally a good thing for the Institute of High Energy Physics to be able to cooperate now.

"Okay." Fabiola Gianotti nodded, then said: "Then let's move on to the next topic..." Tang Yifang also sat down.

However, at this moment, the cell phone in his pocket suddenly vibrated.

He frowned. Who would call him at this time?

When he took it out and looked at it, he was stunned. The person who called was actually Xiao Yi?

Xiao Yi did not come here with them, but remained in the country.

But why was he making this call?
He answered the phone, covered the microphone and whispered: "Xiao Yi, what's wrong? I'm in a meeting now, as I told you before."

Then Xiao Yi's voice came from the other end of the phone: "Has CERN decided to continue verifying the mass of the W boson?"

"Yes." Tang Yifang asked, "Is there any problem with this?"

Then, Xiao Yi said, "Well... please help me convey my suggestion. I think it may not make much sense to continue studying the mass of the W boson. Judging from the current performance of the LHC, it should be impossible to find the real reason why the W boson is overweight."

Tang Yifang was stunned for a moment, and even raised his voice unintentionally: "What?"

It just so happened that Director-General Gianotti had just announced the next agenda item and was waiting for everyone to express their opinions. The meeting room was very quiet, so his voice seemed particularly abrupt.

Gianotti turned his head and asked, "Professor Tang, do you have any questions?"

Tang Yifang pointed to his phone awkwardly, and then said a few words into the microphone. Just when everyone was wondering if he was so presumptuous to call during a meeting, Tang Yifang stood up and said apologetically, "I'm sorry to bother you all. Xiao Yi called me. He has a suggestion that he wants me to pass on to you all."

Now everyone was stunned, Xiao Yi?

So everyone who had originally been quite dissatisfied in their hearts no longer blamed Tang Yifang for interrupting them.

As the first discoverer of the W boson's overmass problem, Xiao Yi has never been to CERN, but his status in their hearts is already extraordinary.

What advice would he give?

"Please go ahead." Secretary-General Fabiola Gianotti also nodded and said.

"Hmm..." Then, Tang Yifang conveyed Xiao Yi's suggestion.

Everyone present was stunned.

what?
Xiao Yi actually suggested that they should not put too much energy on this issue for the time being?
My goodness, he was the first to discover this problem, and now it has attracted unprecedented attention from the physics community, and now he comes up and says he wants to put on the brakes?
Everyone felt confused.

Professor Frank Wilczek narrowed his eyes and said, "Professor Tang, Xiao Yi said that with the current collision energy of the LHC, it is impossible to find the reason why the W boson is abnormal?"

"Yes." Tang Yifang nodded.

"Did he discover something?"

Tang Yifang took out his phone again and had a conversation with Xiao Yi on the other end of the line. Finally, he said, "Xiao Yi said that if he could participate via video now, he could give everyone a simple explanation of the reason. If it is not convenient, it may take a few months for him to give a complete explanation."

Suddenly, there were bursts of discussions in the conference room again.

Fabiola Gianotti pondered for a moment, and finally said: "As the Director-General, I agree with this matter. If any researchers on the scene have any objections, please raise your hands."

Offstage, all the participants shook their heads and no one raised their hands.

"Then, please tell Xiao Yi, Professor Tang, that we agree that he can explain the reason to us via video."

"Ok."

Tang Yifang nodded.

After some quick coordination, Xiao Yi successfully connected to their meeting site.

Xiao Yi's face appeared on the multimedia screen in the conference room, and the environment behind him showed that he was in the dormitory.

He waved towards the camera and asked, "Can you hear me?"

Fabiola Gianotti nodded at him and said, "Hello, Xiao Yi. I am Fabiola Gianotti, Director General of CERN. We can all hear you. Next, please explain to us why you made that suggestion."

"That's good." Xiao Yi nodded with a smile, and then said, "Hello, Director-General Gianotti and all the researchers at CERN."

"First of all, I would like to apologize for interrupting your meeting."

"Regarding that suggestion, I will then need to use the methods of mathematical physics to explain it."

"First, we all know that the mass of the W boson is imparted by the Higgs mechanism through spontaneous symmetry breaking."

"So, we first introduce the Higgs field based on the SU(2)L×U(1)Y gauge symmetry."

Xiao Yi turned around and began his demonstration on a small blackboard behind him - this small blackboard was something he asked the research institute for some time ago.

"The Higgs field is a (2)SU(2) complex scalar doublet = (+, 0) where:"

【+=1/√2(1+i2)，0=1/√2(3+i4)。】

"We then choose the potential energy of the Higgs field to be of the following form."

【V()=μ^2^+λ()^2
Where μ^2 and λ are greater than 0. 】

"After that, we minimize the potential energy V(), and the Higgs field obtains a non-zero vacuum expectation value, causing the symmetry to be broken..."

Xiao Yi began to slowly deduce and gradually demonstrated how the W boson acquired mass through the Higgs mechanism.

"Finally, we calculated the kinetic energy term of the Higgs field through the action of the covariant derivative and substituted the VEV of the Higgs field to generate the mass term, thereby determining the mass of the W boson."

"So far, the derivation process is exactly the same as that in the past in the physics community, and there seems to be no difference. But why is there a problem with the mass of the W boson in the end? Please see if I introduce a new vector field once again in the step of breaking the symmetry of the Higgs mechanism."

"As for this vector field, it comes from the topological quantum field theory of Yang-Mills equations."

"Now, we construct an anti-self-dual Yang-Mills field on the four-dimensional sphere S^4, which satisfies the following conditions."

【F=*F】

"Where F is the curvature form of the Yang-Mills field and * is the Hodge dual operator."

"As we all know, in the four-dimensional case, we can connect it to the four-dimensional Yang-Mills theory by introducing boundary conditions and topological invariants, and similarly, we can also substitute it into the process of symmetry breaking of the Higgs mechanism..."

Hearing Xiao Yi's words, Frank Wilczek and Edward Witten in the conference room both narrowed their eyes.

George Parisi was also present, and he looked surprised: "Is this... a new kind of field!?"

As soon as he said this, the atmosphere in the conference room was immediately ignited.

Originally, quite a number of people were confused when faced with Xiao Yi's processes. The mathematical logic was too complicated, and the methods used were beyond the imagination of most people. Therefore, they could not understand the meaning of these derivation processes.

However, George Parisi's words gave a very accurate explanation of Xiao Yi's deductions:

The "culprit" that causes the W boson to be overweight may come from a "field" that has never been discovered by the physics community in the past? !

Then, Xiao Yi also responded to this as if by coincidence: "... with the introduction of this anti-self-dual field, after reconciling the spontaneous symmetry breaking of the Higgs mechanism, we can find that it not only becomes harmonious, but also has an incomparable mathematical beauty."

"And, with this new process, we can easily calculate the new mass of the W boson, which is 80429 MeV!"

In the conference room, everyone's eyes showed disbelief and shock.

In this way, it fits right!

This almost successfully explains why the W boson is super heavy!

And what does a new field represent?
Maybe it is another elementary particle, or maybe it is a disruptive discovery of a fundamental force that has never been discovered, and of course, it may be the supersymmetric particle that the physics community has been pursuing.

The conference room was eerily quiet. Almost everyone opened their mouths in amazement at the result.

Even Tang Yifang had never expected that Xiao Yi's simple suggestion would lead them to such an unbelievable discovery.

In the conference room, only Xiao Yi's voice was heard.

"…so in the end, we can conclude that the field has the following properties: it interacts strongly with the W boson at very high energies, it exhibits an extremely weak interaction at normal energies, and finally, it may be a unified medium for strong and weak interactions."

Xiao Yi smiled shyly: "Regarding this field, before we can fully understand what it is, I will temporarily name it X field, or Xiao field."

"If it is eventually proven to be a supersymmetric particle, then the name X-field will naturally be eliminated."

"Finally, back to the beginning, the reason why I suggest that you don't continue to spend time and energy studying the mass of the W boson is because it is as difficult to determine whether it really exists through a particle accelerator as it is for supersymmetric particles. The only thing to be thankful for is that we can indirectly determine its existence through the mass of the W boson."

"Therefore, the resources of particle accelerators might be better used to study other topics, which might be more valuable."

"Well, I'm done. Does anyone have any questions?"

(End of this chapter)